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Second order slow drift responses

In document Ahmed, To my brother and sisters (halaman 38-43)

2.4 R ESEARCH DIRECTIONS

2.4.1 Second order slow drift responses

The research on spar platforms began during the 1990’s. Since that time, many numerical and experimental studies have been conducted to investigate the dynamic characteristics of spar platform. Most of the early numerical studies were applied to

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the first generation spar, namely classic spar. These studies were validated by an extensive experimental work conducted on the Joint Industry Project (JIP) Spar under Johnson [18] at the Offshore Technology Research Center (OTRC). The responses of the spar buoy at the wave frequency, even near the spectrum peak frequency were small, but relatively large near its natural frequencies, although elevation measurements showed that the incident waves had insignificant energy at these low frequencies. It was shown that the large-amplitude slow drift motions are induced by second order difference frequency wave loading due to nonlinear wave-wave and wave-body interactions [19-20].

Second order wave loading has mostly been computed using the second order diffraction theory [21-22]. As an example, the JIP Spar motions were calculated by Ran et al. [23] using higher order boundary element method (HOBEM) [24]. Several nonlinearities such as computations in the instantaneous displaced position, nonlinear drag damping, and wave drift damping were considered. It was found that the linear body interaction theory alone was not adequate, and the second order wave-body interaction theory had to be used for the reliable motion prediction of a spar. The resulting numerical results agreed well with the measurements data. But the method is often computationally intensive and thus may not be suitable for parametric studies in the preliminary designs.

A simplified alternative approach is to compute the second order wave loading based on the slender body approximation [25], that is, without explicitly considering the diffraction and radiation effects due to the presence of the structure. It can be applied when inertia effects are important and the structure dimension is small compared to the characteristic design wave length. In this method, the second order difference frequency inertia force was obtained from the complete description of the second order acceleration field which includes both temporal and convective terms.

Additional second order contributions due to the axial divergence and fluctuation of the free surface were also included. The slender body analysis was applied to the computation of the slow varying pitch moments on an articulated loading platform (ALP) and the results agree well with the second order diffraction computation. This

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method was found to be several order faster compared to the second order diffraction theory.

For a typical deepwater offshore structure such as the spar, the ratio of the structure dimension to the characteristic design wave length is usually small (less than 0.2). Hence it may be assumed that the wave field is virtually undisturbed by the structure and that the modified Morison equation [26] is adequate to calculate the first and second order wave exciting forces. Based on this assumption, a new methodology [27] was developed to predict slow drift responses of slender compliant offshore structures due to ocean waves. Hybrid wave model [28] and Morison equation were used to predict the wave kinematics and wave forces respectively for irregular waves.

The results of the numerical method achieved good agreement with experimental measurements for classic spar and floating jacket platforms.

Based on the slender body approximation method, several studies demonstrated the importance of the second order low frequency forces. Mekha et al. [29-30] and Johnson et al. [31] studied the behavior of spar in deep water. In their work, they used Morison equation to calculate the wave forces in time domain considering several second order effects and wave kinematics. They also investigated the effect of neglecting the hydrodynamic forces acting on the mooring lines by modeling them as nonlinear springs. In their studies, they used regular, bichromatic and random waves to predict the responses which are compared with the experimental results showing the effect of each individual second order effect on the spar responses. However, in their studies they neglected the second order temporal acceleration in the analysis. An interesting result [32] was that some of these effects acted in opposite direction, therefore inclusion/exclusion of any of them gave entirely different numerical predictions. Weggel and Roesset [33-34] did similar work using second order diffraction theory implementing WAMIT [35], TFPOP [36] as well as an approximation suggested by Donley and Spanos [37].

Slender body approximation method proves to be an attractive analysis tool for spar which is subjected to various environmental conditions. This was shown by a study [38] concerned with the nonlinear response of a spar platform under different

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environmental conditions, i.e., regular wave, bichromatic, random waves and current using a time domain simulation model. The model could consider several nonlinear effects. Hydrodynamic forces and moments were computed using the Morison equation. It was concluded that Morison equation combined with accurate prediction of wave particle kinematics and force calculations in the displaced position of the platform gave a reliable prediction of platform response both in wave frequency and low frequency range.

A study [39] on the motions of a truss spar based on the full slender body formulation incorporating all nonlinear terms were conducted. For this purpose, a code written in MATLAB was developed by extending the code for classic spar.

Satisfactory agreement was achieved between the predicted results and limited experiment results. In addition, different simplified methods for estimating the forces on the truss section and the hard tank were studied. It was found that only the full slender body formulation could lead to reasonable results.

At the same time, wave kinematics methods were subjected to intensive investigations. A methodology has been developed [40] to establish second order corrections to the engineering methods, which are used to calculate the wave kinematics. The purpose was to find a description of the wave kinematics which predicts measured behavior with good degree of accuracy. The methodology has been applied to the engineering methods proposed by Wheeler [9] and Chakrabarti [10].

The second order Chakrabarti approximation demonstrates good agreement with measured wave kinematics.

A new hybrid wave model (HWM) for the prediction of the wave kinematics of the unidirectional irregular wave train was introduced by Zhang et al. [28]. HWM is different from the other approaches by decomposition of the observed wave elevation into ‘free’ waves up to second order accuracy while the conventional methods consider the wave elevations to be only linear combinations of individual sinusoids.

The numerical model was extensively examined using various wave spectra and was found to be convergent and accurate. The application of the HWM were demonstrated by comparison with two sets of laboratory measurements and with the linear random wave theory and its stretching and extrapolation modification by Spell [41]. It was

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concluded that the HWM is more accurate and reliable than the linear random wave theory especially near steep wave crest.

The differences between various approximate methods to compute the wave kinematics and forces acting on a spar platform up to the instantaneous free water surface was investigated [42]. Three types of procedures were considered; i.e., extrapolation, stretching and the hybrid wave model. Of particular interest for the dynamic response of a spar are the nonlinear low frequency forces. The effects of the different procedures were compared analytically and numerically for the inertia forces using Morison equation [26] as reported in 1950, but the conclusions can be extended to diffraction theory formulations.

A method for resolving incident free-wave components from wave elevations measured around a spar offshore platform [43] was discussed. The importance of this method was proven by comparison between full scale measurements of motions for the Moomvang Truss Spar and the analytical predictions. Particular attention was given to the wave frequency responses. Results revealed an excellent match between the measured and analytically predicted spar responses when the measured waves were adequately decomposed into incident free-wave components and inserted into the numerical model.

The spar motion characteristics in directional wave environment were studied [44]

using the unidirectional hybrid wave model (UHWM) and directional hybrid wave model (DHWM). Comparisons between numerical results from these two different wave models indicated that the slow drifting surge and pitch motions based on DHWM are slightly smaller than those based on UHWM. The slow drifting heave motions from the two wave models were almost the same because the heave motion was mainly excited by the pressure applied on the structure bottom and the predicted bottom pressure from the two methods had almost no differences.

A study by Chitrapu et al. [45] discussed the motion response of a large diameter spar platform in long crested and random directional waves and current using a time domain simulation model. Several nonlinearities such as the free surface force calculation, displaced position force computation, nonlinearities in the equation of

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motion and the effect of wave current interaction were considered for determining the motion response. The effect of wave directionality on the predicted surge and pitch response of the spar platform was studied. It was seen that both wave-current interaction and directional spread of wave energy had a significant effect on the predicted response.

Results from a study [46] on the dynamic response analysis of spar platform subjected to wave and wind forces were presented. The motions considered were surge and pitch. The wind gust was modeled with the Harris [47] and Ochi and Shin [48] wind gust spectra. The effect of the wave age on the wind gust spectrum was included by adopting the Volkov wave age dependent sea surface roughness parameter. The wave age independent Charnock roughness parameter was also used.

The results demonstrated clear effects of wave age on the dynamic response.

Moreover, for high mean wind speeds the total wind response was much smaller than the wave response but for low speeds the wind appeared to be more important.

With respect to the method of analysis, Halkyard [14] stated that the time domain analysis is most appropriate for response predictions in survival conditions while frequency domain analysis is more appropriate for operational conditions. Iftekhar [49] studied the differences between time domain and frequency domain analysis in predicting the slow drift responses of the spar by using Morison equation. The limitation of the frequency domain in modeling the nonlinearities in the exciting forces and the structural properties was shown.

In document Ahmed, To my brother and sisters (halaman 38-43)